文章基本信息

标题：Birth-jump processes and application to forest fire spotting
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作者：T. Hillen ; B. Greese ; J. Martin 等
期刊名称：Journal of Biological Dynamics
印刷版ISSN：1751-3758
电子版ISSN：1751-3766
出版年度：2015
卷号：9
期号：Supp 1
页码：104-127
DOI：10.1080/17513758.2014.950184
出版社：Taylor & Francis
摘要：Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction–diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction–diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of forest fire spread through spotting. We show that spotting increases the invasion speed of a forest fire front.
关键词：birth; jump processes ; integro; differential equations ; diffusion limit ; reaction–diffusion equations ; critical domain size ; minimal wave speed ; wildfire spotting